Transverse vibration analysis of a single-walled carbon nanotube under a random load action

The paper presents the dynamic model of a nanobeam loaded by a uniformly distributed random load, which is considered as a nonstationary stochastic process. The equation of motion is derived on the basis of non-local elasticity theory by using the Galerkin Finite Element Method. Probabilistic characteristics, in the form of time histories of the expected values and standard deviations of dynamic displacements, are computed applying Monte Carlo simulations and the Newmark method. The formulated algorithm is verified within the scope of the eigenvalue problem with a strict solution. A very good agreement is found. The influence of load standard deviation and non-local parameters on dynamic response is considered on the example of a clamped-clamped single-walled carbon nanotube (SWCNT). The obtained results show that random load perturbations should not be a priori neglected in dynamic analyses. The dispersion of displacements, caused by stochastic loads, can be greater than would be expected considering the level of deviations of applied loads.